103 (number)

Not to be confused with 103 AD or 103 BC.

← 102 103 104 →
← 100 101 102 103 104 105 106 107 108 109 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred three
Ordinal	103rd (one hundred third)
Factorization	prime
Prime	27th
Greek numeral	ΡΓ´
Roman numeral	CIII, ciii
Binary	11001112
Ternary	102113
Senary	2516
Octal	1478
Duodecimal	8712
Hexadecimal	6716

103 (one hundred [and] three) is the natural number following 102 and preceding 104.

In mathematics

103 is a prime number, and the largest prime factor of ${\displaystyle 6!+1=721=7\cdot 103}$. ^[1] The previous prime is 101. This makes 103 a twin prime. ^[2] It is the fifth irregular prime, ^[3] because it divides the numerator of the Bernoulli number $${\displaystyle B_{24}=-{\frac {236364091}{2730}}=-{\frac {103\cdot 2294797}{2730}}.}$$

The equation ${\displaystyle 64^{3}+94^{3}=103^{3}+1}$ makes 103 part of a "Fermat near miss". ^[4]

There are 103 different connected series-parallel partial orders on exactly six unlabeled elements. ^[5]

103 is conjectured to be the smallest number for which repeatedly reversing the digits of its ternary representation, and adding the number to its reversal, does not eventually reach a ternary palindrome. ^[6]

References

1. Sloane, N. J. A. (ed.). "SequenceA002583(Largest prime factor of n! + 1)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA001097(Twin primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA000928(Irregular primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Sloane, N. J. A. (ed.). "SequenceA050791(Consider the Diophantine equation x^3 + y^3 = z^3 + 1 (1 < x < y < z) or 'Fermat near misses'. Sequence gives values of z in monotonic increasing order.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Sloane, N. J. A. (ed.). "SequenceA007453(Number of unlabeled connected series-parallel posets with n nodes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. Sloane, N. J. A. (ed.). "SequenceA066450(Conjectured value of the minimal number to which repeated application of the "reverse and add!" algorithm in base n does not terminate in a palindrome)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.